A367276 - OEIS

A367276

Place n equally spaced points on each side of a square, and join each of these points by a chord to the 3*n new points on the other three sides: sequence gives number of vertices in the resulting planar graph.

4, 9, 69, 345, 1337, 2885, 7445, 12833, 23365, 36589, 64669, 80133, 138313, 176885, 233765, 312013, 455273, 513277, 741965, 819589, 1046245, 1310761, 1692961, 1772097, 2315289, 2713997, 3165125, 3552753, 4538845, 4602985, 6015561, 6432681, 7421345, 8550485, 9439621, 10063993, 12635769

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

We start with the four corner points of the square, and add n further points along each edge. Including the corner points, we end up with n+2 points along each edge, and the edge is divided into n+1 line segments.

Each of the n points added to an edge is joined by 3*n chords to the points that were added to the other three edges. There are 6*n^2 chords.

LINKS

Table of n, a(n) for n=0..36.

Scott R. Shannon, Image for n = 1.

Scott R. Shannon, Image for n = 2.

Scott R. Shannon, Image for n = 3.

Scott R. Shannon, Image for n = 4.

Scott R. Shannon, Image for n = 5.

Scott R. Shannon, Image for n = 10.

FORMULA

a(n) = A367279(n) - A367278(n) + 1 (Euler).

CROSSREFS

Cf. A367277 (interior vertices), A367278 (regions), A367279 (edges).

If the 4*n points are placed "in general position" instead of uniformly, we get sequences A334698, A367121, A367122.

If the 4*n points are placed uniformly and we also draw chords from the four corner points of the square to these 4*n points, we get A255011, A331448, A331449, A334690.

Sequence in context: A220189 A122956 A041777 * A100517 A392980 A327579

Adjacent sequences: A367273 A367274 A367275 * A367277 A367278 A367279

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Nov 11 2023

STATUS

approved